A Hadamard type theorem for the space-time.
A model of gauge theory with invariant variables.
An introduction to the Einstein-Vlasov system
Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system
We consider the spherically symmetric Vlasov-Einstein system in the case of asymptotically flat spacetimes. From the physical point of view this system of equations can model the formation of a spherical black hole by gravitational collapse or describe the evolution of galaxies and globular clusters. We present high-order numerical schemes based on semi-Lagrangian techniques. The convergence of the solution of the discretized problem to the exact solution is proven and high-order error estimates...
Around the bounded curvature conjecture in general relativity
We report on recent progress obtained on the construction and control of a parametrix to the homogeneous wave equation , where is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes bounds on the curvature tensor of is a major step towards the proof of the bounded curvature conjecture.